We consider the problem of time series forecasting in an adaptive setting. We focus on the inference of state-space models under unknown and potentially time-varying noise variances. We introduce an augmented model in which the variances are represented as auxiliary gaussian latent variables in a tracking mode. As variances are nonnegative, a transformation is chosen and applied to these latent variables. The inference relies on the online variational Bayesian methodology, which consists in minimizing a Kullback-Leibler divergence at each time step. We observe that the minimum of the Kullback-Leibler divergence is an extension of the Kalman filter taking into account the variance uncertainty. We design a novel algorithm, named Viking, using these optimal recursive updates. For auxiliary latent variables, we use second-order bounds whose optimum admit closed-form solutions. Experiments on synthetic data show that Viking behaves well and is robust to misspecification.
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A central challenge in data-driven model discovery is the presence of hidden, or latent, variables that are not directly measured but are dynamically important. Takens' theorem provides conditions for when it is possible to augment these partial measurements with time delayed information, resulting in an attractor that is diffeomorphic to that of the original full-state system. However, the coordinate transformation back to the original attractor is typically unknown, and learning the dynamics in the embedding space has remained an open challenge for decades. Here, we design a custom deep autoencoder network to learn a coordinate transformation from the delay embedded space into a new space where it is possible to represent the dynamics in a sparse, closed form. We demonstrate this approach on the Lorenz, R\"ossler, and Lotka-Volterra systems, learning dynamics from a single measurement variable. As a challenging example, we learn a Lorenz analogue from a single scalar variable extracted from a video of a chaotic waterwheel experiment. The resulting modeling framework combines deep learning to uncover effective coordinates and the sparse identification of nonlinear dynamics (SINDy) for interpretable modeling. Thus, we show that it is possible to simultaneously learn a closed-form model and the associated coordinate system for partially observed dynamics.
Convolutional neural networks (CNNs) have been successfully applied to the single target tracking task in recent years. Generally, training a deep CNN model requires numerous labeled training samples, and the number and quality of these samples directly affect the representational capability of the trained model. However, this approach is restrictive in practice, because manually labeling such a large number of training samples is time-consuming and prohibitively expensive. In this paper, we propose an active learning method for deep visual tracking, which selects and annotates the unlabeled samples to train the deep CNNs model. Under the guidance of active learning, the tracker based on the trained deep CNNs model can achieve competitive tracking performance while reducing the labeling cost. More specifically, to ensure the diversity of selected samples, we propose an active learning method based on multi-frame collaboration to select those training samples that should be and need to be annotated. Meanwhile, considering the representativeness of these selected samples, we adopt a nearest neighbor discrimination method based on the average nearest neighbor distance to screen isolated samples and low-quality samples. Therefore, the training samples subset selected based on our method requires only a given budget to maintain the diversity and representativeness of the entire sample set. Furthermore, we adopt a Tversky loss to improve the bounding box estimation of our tracker, which can ensure that the tracker achieves more accurate target states. Extensive experimental results confirm that our active learning-based tracker (ALT) achieves competitive tracking accuracy and speed compared with state-of-the-art trackers on the seven most challenging evaluation benchmarks.
Estimating and reacting to external disturbances is of fundamental importance for robust control of quadrotors. Existing estimators typically require significant tuning or training with a large amount of data, including the ground truth, to achieve satisfactory performance. This paper proposes a data-efficient differentiable moving horizon estimation (DMHE) algorithm that can automatically tune the MHE parameters online and also adapt to different scenarios. We achieve this by deriving the analytical gradient of the estimated trajectory from MHE with respect to the tuning parameters, enabling end-to-end learning for auto-tuning. Most interestingly, we show that the gradient can be calculated efficiently from a Kalman filter in a recursive form. Moreover, we develop a model-based policy gradient algorithm to learn the parameters directly from the trajectory tracking errors without the need for the ground truth. The proposed DMHE can be further embedded as a layer with other neural networks for joint optimization. Finally, we demonstrate the effectiveness of the proposed method via both simulation and experiments on quadrotors, where challenging scenarios such as sudden payload change and flying in downwash are examined.
We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance matrices as they admit a latent factor based representation that allows easy inference. The same is however not true for precision matrices due to the lack of computationally convenient representations which restricts inference to low-to-moderate dimensional problems. We address this remarkable gap in the literature by building on a latent variable representation for such decomposition for precision matrices. The construction leads to an efficient Gibbs sampler that scales very well to high-dimensional problems far beyond the limits of the current state-of-the-art. The ability to efficiently explore the full posterior space also allows the model uncertainty to be easily assessed. The decomposition crucially additionally allows us to adapt sparsity inducing priors to shrink the insignificant entries of the precision matrix toward zero, making the approach adaptable to high-dimensional small-sample-size sparse settings. Exact zeros in the matrix encoding the underlying conditional independence graph are then determined via a novel posterior false discovery rate control procedure. A near minimax optimal posterior concentration rate for estimating precision matrices is attained by our method under mild regularity assumptions. We evaluate the method's empirical performance through synthetic experiments and illustrate its practical utility in data sets from two different application domains.
The great success of deep learning (DL) has inspired researchers to develop more accurate and efficient symbol detectors for multi-input multi-output (MIMO) systems. Existing DL-based MIMO detectors, however, suffer several drawbacks. To address these issues, in this paper, we develop a model-driven DL detector based on variational Bayesian inference. Specifically, the proposed unrolled DL architecture is inspired by an inverse-free variational Bayesian learning framework which circumvents matrix inversion via maximizing a relaxed evidence lower bound. Two networks are respectively developed for independent and identically distributed (i.i.d.) Gaussian channels and arbitrarily correlated channels. The proposed networks, referred to as VBINet, have only a few learnable parameters and thus can be efficiently trained with a moderate amount of training samples. The proposed VBINet-based detectors can work in both offline and online training modes. An important advantage of our proposed networks over state-of-the-art MIMO detection networks such as OAMPNet and MMNet is that the VBINet can automatically learn the noise variance from data, thus yielding a significant performance improvement over the OAMPNet and MMNet in the presence of noise variance uncertainty. Simulation results show that the proposed VBINet-based detectors achieve competitive performance for both i.i.d. Gaussian and realistic 3GPP MIMO channels.
The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this work, we show that it suffices to perform inference over a small subset of model weights in order to obtain accurate predictive posteriors. The other weights are kept as point estimates. This subnetwork inference framework enables us to use expressive, otherwise intractable, posterior approximations over such subsets. In particular, we implement subnetwork linearized Laplace: We first obtain a MAP estimate of all weights and then infer a full-covariance Gaussian posterior over a subnetwork. We propose a subnetwork selection strategy that aims to maximally preserve the model's predictive uncertainty. Empirically, our approach is effective compared to ensembles and less expressive posterior approximations over full networks.
Discovering causal structure among a set of variables is a fundamental problem in many empirical sciences. Traditional score-based casual discovery methods rely on various local heuristics to search for a Directed Acyclic Graph (DAG) according to a predefined score function. While these methods, e.g., greedy equivalence search, may have attractive results with infinite samples and certain model assumptions, they are usually less satisfactory in practice due to finite data and possible violation of assumptions. Motivated by recent advances in neural combinatorial optimization, we propose to use Reinforcement Learning (RL) to search for the DAG with the best scoring. Our encoder-decoder model takes observable data as input and generates graph adjacency matrices that are used to compute rewards. The reward incorporates both the predefined score function and two penalty terms for enforcing acyclicity. In contrast with typical RL applications where the goal is to learn a policy, we use RL as a search strategy and our final output would be the graph, among all graphs generated during training, that achieves the best reward. We conduct experiments on both synthetic and real datasets, and show that the proposed approach not only has an improved search ability but also allows a flexible score function under the acyclicity constraint.
We study active object tracking, where a tracker takes as input the visual observation (i.e., frame sequence) and produces the camera control signal (e.g., move forward, turn left, etc.). Conventional methods tackle the tracking and the camera control separately, which is challenging to tune jointly. It also incurs many human efforts for labeling and many expensive trial-and-errors in realworld. To address these issues, we propose, in this paper, an end-to-end solution via deep reinforcement learning, where a ConvNet-LSTM function approximator is adopted for the direct frame-toaction prediction. We further propose an environment augmentation technique and a customized reward function, which are crucial for a successful training. The tracker trained in simulators (ViZDoom, Unreal Engine) shows good generalization in the case of unseen object moving path, unseen object appearance, unseen background, and distracting object. It can restore tracking when occasionally losing the target. With the experiments over the VOT dataset, we also find that the tracking ability, obtained solely from simulators, can potentially transfer to real-world scenarios.
Existing visual tracking methods usually localize a target object with a bounding box, in which the performance of the foreground object trackers or detectors is often affected by the inclusion of background clutter. To handle this problem, we learn a patch-based graph representation for visual tracking. The tracked object is modeled by with a graph by taking a set of non-overlapping image patches as nodes, in which the weight of each node indicates how likely it belongs to the foreground and edges are weighted for indicating the appearance compatibility of two neighboring nodes. This graph is dynamically learned and applied in object tracking and model updating. During the tracking process, the proposed algorithm performs three main steps in each frame. First, the graph is initialized by assigning binary weights of some image patches to indicate the object and background patches according to the predicted bounding box. Second, the graph is optimized to refine the patch weights by using a novel alternating direction method of multipliers. Third, the object feature representation is updated by imposing the weights of patches on the extracted image features. The object location is predicted by maximizing the classification score in the structured support vector machine. Extensive experiments show that the proposed tracking algorithm performs well against the state-of-the-art methods on large-scale benchmark datasets.
Current convolutional neural networks algorithms for video object tracking spend the same amount of computation for each object and video frame. However, it is harder to track an object in some frames than others, due to the varying amount of clutter, scene complexity, amount of motion, and object's distinctiveness against its background. We propose a depth-adaptive convolutional Siamese network that performs video tracking adaptively at multiple neural network depths. Parametric gating functions are trained to control the depth of the convolutional feature extractor by minimizing a joint loss of computational cost and tracking error. Our network achieves accuracy comparable to the state-of-the-art on the VOT2016 benchmark. Furthermore, our adaptive depth computation achieves higher accuracy for a given computational cost than traditional fixed-structure neural networks. The presented framework extends to other tasks that use convolutional neural networks and enables trading speed for accuracy at runtime.
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